Question

Find the maximum value of the function f(x,y) = 2x - 5(y^2) subject to the constraint (x^2)+5(y^2) = 25.

Answer #1

Find the minimum value of the function f(x,y)=2x+y, subject to
the constraint x2+y2=5.

The function f(x,y,z)= 4x+z^2 has an absolute maximum and
minimum values subject to the constraint of 2x^2+2y^2+3z^2=50. Use
Lagrange multipliers to find these values.

The function f(x,y)=4x-4y has an absolute maximum value and
absolute minimum value subject to the constraint x^2-xy+y^2=9. Use
Lagrange multipliers to find these values.

Find the relative maximum value of
f(x,y)=x2-9y2, subject to the constraint
x-y=24
The relative maximum value is f(_,_) = _

Find the indicated maximum or minimum value of f subject to the
given constraint.
Minimum: f(x,y)=2 x^2 + y ^2 + 2 xy + 3 x + 2 y
; y^2 = x + 1
The minimum value is -------------.
(Type an integer or a simplified fraction.)

Find the relative maximum value of f(x,y,z)=xyz2,
subject to the constraint x+y+5z=6
The Relative Maximum value is f(_,_,_)=_

Find the indicated maximum or minimum value of f subject to the
given constraint. Maximum: f(x,y,z) = (x2)(y2)(z2); x2 + y2 + z2
= 6

Find the extremum of f(x,y) subject to the given constraint,
and state whether it is a maximum or a minimum. f(x,y)=4y^2-12x^2;
2x+y=8.

Find the maximum and minimum of the function f (x, y) = 6x − 2y
subject to the constraint . 3x^2 + y ^2 = 4

Use the method of Lagrange Multipliers to find the maximum value
of the function f(x,y)= x^3y^2 subject to the constraint
x^2+y^2=10.

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